By performing the coding scheme in [1]}, [2]}, [3]}, [4]}, an achievable rate region can be characterized by the matrix optimization problem
\(\max _{(R_{0},R_{1}, R_{2}) \in \mathcal {C}(\mathbf {S})} R_{0} + \mu _{2}R_{2} + \mu _{1} R_{1} \ge R^{*}(S, \mu _1, \mu _2), \quad 0 < \mu _{1} \le \mu _{2} < 1,\) 
